Symmetric deformed binomial distributions: An analytical example where the Boltzmann-Gibbs entropy is not extensive

@article{Bergeron2016SymmetricDB,
title={Symmetric deformed binomial distributions: An analytical example where the Boltzmann-Gibbs entropy is not extensive},
author={H. Bergeron and E. Curado and J. Gazeau and L. M. Rodrigues},
journal={Journal of Mathematical Physics},
year={2016},
volume={57},
pages={023301}
}

Asymptotic behavior (with respect to the number of trials) of symmetric generalizations of binomial distributions and their related entropies is studied through three examples. The first one has the q-exponential as the generating function, the second one involves the modified Abel polynomials, and the third one has Hermite polynomials. We prove analytically that the Renyi entropy is extensive for these three cases, i.e., it is proportional (asymptotically) to the number n of events and that q… CONTINUE READING